Theorems · Theorem · functional analysis
lp.norm_const_smul
∀ {𝕜 : Type u_1} {α : Type u_3} {E : α → Type u_4} {p : ENNReal} [inst : (i : α) → NormedAddCommGroup (E i)]
[inst_1 : NormedDivisionRing 𝕜] [inst_2 : (i : α) → Module 𝕜 (E i)] [inst_3 : ∀ (i : α), IsBoundedSMul 𝕜 (E i)],
p ≠ 0 → ∀ {c : 𝕜} (f : ↥(lp E p)), ‖c • f‖ = ‖c‖ * ‖f‖- Defined in
- Mathlib.Analysis.Normed.Lp.lpSpace
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 226 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites23
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement and proof · cited by 25,697
- Modulestatement and proof · cited by 20,661
- NormedAddCommGroupstatement and proof · cited by 15,752
- ENNRealstatement and proof · cited by 9,879
- Norm.normstatement and proof · cited by 5,413
- AddSubgroupstatement · cited by 3,232
- le_antisymmproof · cited by 2,068
- MulZeroClass.zero_mulproof · cited by 1,625
- eq_or_neproof · cited by 1,117
- norm_nonnegproof · cited by 725
- zero_smulproof · cited by 716
- norm_zeroproof · cited by 366
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